Efficient bipartite quantum state purification in arbitrary dimensional Hilbert spaces

A new purification scheme is proposed which applies to arbitrary dimensional bipartite quantum systems. It is based on the repeated application of a special class of nonlinear quantum maps and a single, local unitary operation. This special class of nonlinear quantum maps is generated in a natural way by a hermitian generalized XOR-gate. The proposed purification scheme offers two major advantages, namely it does not require local depolarization operations at each step of the purification procedure and it purifies more efficiently than other know purification schemes.Comment: This manuscript is based on results of our previous manuscript 'Generalized quantum XOR-gate for quantum teleportation and state purification in arbitrary dimensional Hilbert spaces

Purification of genuine multipartite entanglement

In tasks, where multipartite entanglement plays a central role, state purification is, due to inevitable noise, a crucial part of the procedure. We consider a scenario exploiting the multipartite entanglement in a straightforward multipartite purification algorithm and compare it to bipartite purification procedures combined with state teleportation. While complete purification requires an infinite amount of input states in both cases, we show that for an imperfect output fidelity the multipartite procedure exhibits a major advantage in terms of input states used.Comment: 5 pages, 2 figure

Monogamy, polygamy, and other properties of entanglement of purification

For bipartite pure and mixed quantum states, in addition to the quantum mutual information, there is another measure of total correlation, namely, the entanglement of purification. We study the monogamy, polygamy, and additivity properties of the entanglement of purification for pure and mixed states. In this paper, we show that, in contrast to the quantum mutual information which is strictly monogamous for any tripartite pure states, the entanglement of purification is polygamous for the same. This shows that there can be genuinely two types of total correlation across any bipartite cross in a pure tripartite state. Furthermore, we find the lower bound and actual values of the entanglement of purification for different classes of tripartite and higher-dimensional bipartite mixed states. Thereafter, we show that if entanglement of purification is not additive on tensor product states, it is actually subadditive. Using these results, we identify some states which are additive on tensor products for entanglement of purification. The implications of these findings on the quantum advantage of dense coding are briefly discussed, whereby we show that for tripartite pure states, it is strictly monogamous and if it is nonadditive, then it is superadditive on tensor product states.Comment: 12 pages, 2 figures, Published versio

Entanglement of purification: from spin chains to holography

Purification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of many degrees of freedom, one natural purification is the one with minimal entanglement. Here we study the entropy of the minimally entangled purification, called the entanglement of purification, in three model systems: an Ising spin chain, conformal field theories holographically dual to Einstein gravity, and random stabilizer tensor networks. We conjecture values for the entanglement of purification in all these models, and we support our conjectures with a variety of numerical and analytical results. We find that such minimally entangled purifications have a number of applications, from enhancing entanglement-based tensor network methods for describing mixed states to elucidating novel aspects of the emergence of geometry from entanglement in the AdS/CFT correspondence.Comment: 40 pages, multiple figures. v2: references added, typos correcte

Entanglement of Purification and Multiboundary Wormhole Geometries

We posit a geometrical description of the entanglement of purification for subregions in a holographic CFT. The bulk description naturally generalizes the two-party case and leads to interesting inequalities among multi-party entanglements of purification that can be geometrically proven from the conjecture. Further, we study the relationship between holographic entanglements of purification in locally-AdS3 spacetimes and entanglement entropies in multi-throated wormhole geometries constructed via quotienting by isometries. In particular, we derive new holographic inequalities for geometries that are locally AdS3 relating entanglements of purification for subregions and entanglement entropies in the wormhole geometries.Comment: 23 pages, 12 figures; v2 added references; v3 fixed inequality direction in Eq.(2), expanded discussion - reflects published versio

Optimized Entanglement Purification

We investigate novel protocols for entanglement purification of qubit Bell pairs. Employing genetic algorithms for the design of the purification circuit, we obtain shorter circuits achieving higher success rates and better final fidelities than what is currently available in the literature. We provide a software tool for analytical and numerical study of the generated purification circuits, under customizable error models. These new purification protocols pave the way to practical implementations of modular quantum computers and quantum repeaters. Our approach is particularly attentive to the effects of finite resources and imperfect local operations - phenomena neglected in the usual asymptotic approach to the problem. The choice of the building blocks permitted in the construction of the circuits is based on a thorough enumeration of the local Clifford operations that act as permutations on the basis of Bell states

Test Case Purification for Improving Fault Localization

Finding and fixing bugs are time-consuming activities in software development. Spectrum-based fault localization aims to identify the faulty position in source code based on the execution trace of test cases. Failing test cases and their assertions form test oracles for the failing behavior of the system under analysis. In this paper, we propose a novel concept of spectrum driven test case purification for improving fault localization. The goal of test case purification is to separate existing test cases into small fractions (called purified test cases) and to enhance the test oracles to further localize faults. Combining with an original fault localization technique (e.g., Tarantula), test case purification results in better ranking the program statements. Our experiments on 1800 faults in six open-source Java programs show that test case purification can effectively improve existing fault localization techniques

The entanglement of purification

We introduce a measure of both quantum as well as classical correlations in a quantum state, the entanglement of purification. We show that the (regularized) entanglement of purification is equal to the entanglement cost of creating a state $\rho$ asymptotically from maximally entangled states, with negligible communication. We prove that the classical mutual information and the quantum mutual information divided by two are lower bounds for the regularized entanglement of purification. We present numerical results of the entanglement of purification for Werner states in ${\cal H}_2 \otimes {\cal H}_2$.Comment: 12 pages RevTex, 1 figure, to appear in JMP special issue on quantum information. v3 contains additional references, motivation, and a small change in the figur

Ponderomotive entanglement purification

It is shown that ponderomotive force can be used to purify entangled states. The protocol is based on the possibility to exploit such force for a local quantum nondemolition measurement of the total excitation number of continuos variable entangled pairs.Comment: 7 pages, 3 figures, ReVTeX, Accepted for publication in Phys. Lett.